User:Boris Tsirelson/Sandbox1

In Euclidean geometry, a line (sometimes called, more explicitly, a straight line) is an abstract concept that models the common notion of a curve that does not bend, has no thickness and extends infinitely in both directions.

It is closely related to other basic concepts of geometry, especially, distance: it provides the shortest path between any two of its points. In space it can also be described as the intersection of two planes.

Assuming an (intuitive or physical) idea of the geometry of a plane, "line" can be defined in terms of distances, orthogonality, coordinates etc. (as we shall do below).

In a more abstract approach (vector spaces) lines are defined as one-dimensional affine subspaces.

In an axiomatic approach, basic concepts of elementary geometry, such as "point" and "line", are undefined primitives.